Estimation of parameters in circuit QED by continuous quantum measurement

TL;DR

This paper demonstrates that in circuit QED, continuous quantum measurement combined with Bayesian estimation can surpass the standard quantum limit in parameter estimation, leveraging quantum correlations over time.

Contribution

It introduces a method to improve parameter estimation precision in circuit QED using Bayesian techniques and measurement design, surpassing the standard quantum limit.

Findings

Estimation precision scales beyond the standard quantum limit with proper measurement design.

Quantum correlations in measurement signals enhance estimation accuracy.

Quantum efficiency impacts the precision scaling behavior.

Abstract

Designing high-precision and efficient schemes is of crucial importance for quantum parameter estimation in practice. The estimation scheme based on continuous quantum measurement is one possible type of this, which looks also the most natural choice in case such as continuous dynamical process. In this work we specify the study to the stat-of-the-art superconducting circuit quantum-electrodynamics (QED) system, where the high-quality continuous measurement has been extensively exploited in the past decade. Within the framework of Bayesian estimation and particularly using the quantum Bayesian rule in circuit QED, we numerically simulate the likelihood function as estimator for the Rabi frequency of qubit oscillation. We find that, by proper design of the interaction strength of measurement, the estimate precision can scale with the measurement time beyond the standard quantum limit, which is usually assumed for this type of continuous measurement since no more special quantum resource is involved. We understand this remarkable result by quantum correlation in time between the output signals, and simulate the effect of quantum efficiency of the measurement on the precision scaling behavior.